As the constraints are differentiable without any critical points, we consider the KKT conditions [1]}, [2]} to obtain the solution for this problem. They are listed as follows:
\(\frac{\partial L}{\partial \alpha }&=a \cos \alpha \sin \beta -b\sin \alpha \sin \beta +c\cos \alpha \cos \beta \nonumber \\&-d\sin \alpha \cos \beta +\lambda _1-\lambda _2=0,\\\frac{\partial L}{\partial \beta }&=a \sin \alpha \cos \beta +b\cos \alpha \cos \beta -c\sin \alpha \sin \beta \nonumber \\&-d\cos \alpha \sin \beta +\lambda _3-\lambda _4=0,\) 
